Design and monitoring of survival trials in complex scenarios

Abstract

This paper proposes an approach to design and monitor survival trials accounting for complex scenarios such as delayed treatment effect, treatment dilution, and treatment crossover. These scenarios often lead to non‐proportional hazards, making study design and monitoring more difficult. We demonstrate that, with event times following piecewise exponential distributions, the log‐rank statistic as well as its variance‐covariance structure can be easily computed, which greatly simplifies study design and monitoring. As the number of pieces in the exponential distributions can be arbitrary, this approach can handle a wide range of scenarios. Three hypothetical examples are used to demonstrate its potential use.

Sample size and power for the weighted log‐rank test and Kaplan‐Meier based tests with allowance for nonproportional hazards

“…We found that most programs provide only calculations for the unweighted or weighted log-rank test. Of these programs, the PWEALL package in R by Luo et al (2019) and the ART module in Stata by Barthel et al (2006) are the most advanced. Both allow users to specify nonuniform accrual, piecewise exponential survival, and flexible loss to follow-up.…”

“…One might jump to the conclusion that, under the more practical assumption of fixed alternatives (eg, PH), ( , 1) leads to less accurate power calculations than ( ,̃2∕ 2 ) and ( ,̃2∕ 2 ). Indeed, Luo et al (2019) make this very conclusion, citing that → ( ,̃2∕ 2 ). However, convergence in distribution for itself requires the assumption of local alternatives (see proof in Web Appendix A.3).…”

“…∼ ( ,̃2∕ 2 ), where = √ Δ∕ . Luo et al (2019) also previously derived the asymptotic variance for . However, their variance estimate-denoted here bỹ2-assumes patients are assigned treatment via simple randomization, that is, s are sampled as Bernoulli random variables with probability 1 .…”

“…We call the above sequence of calculating sample and event size the n-d method because, contrary to the d-n method, is calculated before . The n-d method has been previously applied in the context of the weighted/unweighted log-rank test (Hasegawa, 2014;Luo et al, 2019). Here, we formalize the method and extend its application to other nonparametric tests.…”

“…Several papers have proposed analytical solutions for sample size and power calculation under NPH. However, most of these solutions apply only to the weighted log-rank test under particular patterns of NPH, for example, piecewise exponential survival (Barthel et al, 2006;Luo et al, 2019), PH cure model (Wang et al, 2011), or delayed treatment effect model (Hasegawa, 2014). It is unclear how these solutions will translate under alternative assumptions (eg, Weibull survival) or when other nonparametric tests are used.…”